People naturally take a while to accept and get comfortable around a new person in any social setting. You'd probably also take a while to get comfortable around them.
This goes a long way towards making yourself come across as friendly and approachable.
Don't stop doing that.
Here are a few rules of thumb I'd recommend:
When walking past someone in a hallway, I'd usually either nod my head or say hello, and they usually respond in kind.
When walking past someone at their desk, I'd do the same as above if they make eye contact, but otherwise I'll probably refrain from potentially distracting them with a greeting.
I may make exceptions for people I talk to regularly or if it's a small office.
When arriving at my desk, I usually give a greeting to:
- the person/people sitting next to me
- whomever's there at the moment
- everyone and no-one in particular
- whomever's attention I've drawn
- or my team
... depending on what makes the most sense to me at the time and probably based on how I feel.
If people don't respond, I usually don't think too much about it. They might just be deep in thought, in the middle of something they can't interrupt or they might just not have heard.
Be positive (on the outside)
- Smile at people
- Be excited about what's happening in your life.
- Be interested in and excited about what's happening in other people's lives.
- Be confident (or appear to be confident; even if I'm feeling awkward and self-conscious, I still make eye contact, smile, speak clearly and try to say what whatever I want to say with conviction)
I know it can be hard if you're introverted, but this goes a long way towards making people want to talk to you.
You don't have to turn into a super bubbly person, nor do these things all the time. Just do them a bit more often (if you're not doing them that much as it stands).
Even just something relatively small like cutting words like "fine", "okay" and "cool" out of your vocabulary and replacing them with words like "awesome" or "great" (or even "terrible", if you delivery it with enough positivity) could make a huge difference. Giving more extensive answers can also help a lot (a minor example: "How's it going?" "Pretty well, but I can't wait for the weekend!").
Here are 3 introverts' dilemmas: (the last one is probably the most relevant to your situation, although the others may also apply)
- Two people like each other (as friends or more), but both are too afraid the other doesn't like them, so neither does anything about it.
- One person likes someone else (as friends or more), but they're too afraid to do anything about it. The other person may be open to something, but has no idea how the first person feels and hasn't thought much about them, so neither does anything about it.
- Someone wants to be a part of a group, and sits back waiting for the group to involve them. The group wouldn't mind if that person were a part of it, but they're not actively trying to be part of it, so the group assumes they're not interested. So no-one does anything about it.
The point you should take from the above is this: don't just sit back and wait for people to include you. Start conversations with people, speak up in group conversations, ask whether you can go along to things if it seems like a more casual affair*, invite people to stuff, etc.
I know being proactive can be hard, but that's how you get what you want in life. It also gets easier the more you do it. I used to basically never talk to anyone outside my team. Now I'd be comfortable striking up a conversation with pretty much anyone who works at my office. I'm still an introvert, but I've just realised and accepted that starting a conversation just isn't such a big deal (after forcing myself to do it once or twice).
* For example, people going to lunch on a workday is usually super casual. If they're meeting at someone's house in the evening or on the weekend, you can potentially still ask about being included, although I'd be a bit more cautious about overstepping my bounds there (especially about how I'd phrase it).
Start with one person
When you have a group of people that know each other, they will often talk about things that require some context to make sense of, so it can be hard to integrate into a group from there.
If you're talking to someone one-on-one, it's much easier to actually be part of the conversation (it's kind of hard not to be) and build a connection.
Make some small talk with someone at the coffee machine or in the hallway or wherever (keeping in mind that you probably shouldn't drag those conversations out too much in case they're on their way to a meeting or they're busy).
You could try to build a strong connection with one person, or you could connect with various people. Either approach could help with gaining acceptance in the group. They may ask you questions or mention something about you in group conversations, which could help you connect with others. Or those connections could just be the goal in and of itself.
Ask questions (but not too many)
If people are talking about things you don't understand in a conversation you're in, it's perfectly fine to ask for some context occasionally.
Try to pick your battles. Don't try to understand everything. Focus on things that seem important and could tell you a lot about the people involved.
You could also hold some of these questions until you get into a one-on-one conversation with them. It probably doesn't make too much sense to ask questions that go into a lot of detail in a group conversation where most people may already know this information.
Try not to worry about it too much though. It's probably going to feel a bit awkward to stop a conversation to ask for context, but most of the time other people won't think much of it.
Invite people to stuff
This could include asking whether someone wants to grab a coffee or it could be hosting or attending some sort of party or event involving mutual interests (ideally, but not necessarily) and inviting others.
You can do this even if you don't know the people all that well.
The interactions and conversations that spontaneously happen can be sufficient to build connections to more naturally lead into these sorts of things. But they also may not be (or it may take really long).
Don't worry (too much) about whether they like you
It's easier said than done, but try not to worry too much.
There are thousands of signals you can analyse in terms of body language, expression, tone, phrasing, etc. to the point that if you're looking hard enough for evidence to support the belief that people don't like you (or any other belief), you'll probably find it. You'll just drive yourself crazy. Most of those signals don't actually mean anything at all.
Try to focus on the more high-level things. Do they occasionally invite you to stuff? If you invite them to stuff, do they occasionally accept your invitation? Do they actually stick around occasionally when you try to talk to them? Keep in mind there are plenty of reasons why they might not do those things, so take those signals with a substantial grain of salt.
Also, try to assume the best. If you incorrectly believe someone likes you, you may just end up bugging them a bit or slightly embarrassing yourself. In the moment it might suck, but in the long term it doesn't matter at all. If you incorrectly believe someone doesn't like you, you may end up losing out on an amazing relationship, and if you keep doing this, you may lose out on all relationships. The latter is much worse. Assume people like you (or they're indifferent towards you) until you have strong evidence to suggest otherwise.
Also, even if they don't have the best opinion of you, there's always the option of changing their mind by just generally being nice to them and being fun to be around.